SSC CHSL 2024 PYQ — Question 61

The correct answer is option 3 i.e. 4.

Given that

√13 sinθ = 2

⇒ sinθ = $\frac{2}{√13}$ 

Sinθ = $\frac{Perpendicular}{Hypotenuse}$

Hence, perpendicular = 2 and hypotenuse = √13

Using Pythagoras theorem we get base = 3  

⇒ Cosθ = $\frac{Base}{Hypotenuse}$ = $\frac{3}{√13}$

⇒ Tanθ = $\frac{Perpendicular}{Base}$ = $\frac{2}{3}$

Substituting the values we get

$\frac{3tanθ + √13sinθ}{√13cosθ - 3tanθ}$ = $\frac{2 + 2}{1}$ = 4

Hence, the value of $\frac{3tanθ + √13sinθ}{√13cosθ - 3tanθ}$ = 4